Count touching neighbors

In this notebook we visualize which cells in a tissue are neighbors by drawing a mesh. Furthermore, we can change the intensity of the mesh so that it corresponds to the distance between the centroids of the cells.

import pyclesperanto_prototype as cle
import numpy as np
import pandas as pd

Test data

Let’s generate some tissue-like structure consisting of cells which typically have approximately 6 neighbors.

cells = cle.artificial_tissue_2d(
    delta_x=48, 
    delta_y=32, 
    random_sigma_x=7, 
    random_sigma_y=7, 
    width=250, 
    height=250)

cle.imshow(cells, labels=True)

Mesh between neighboring cells

Before counting neighbors, we should visualize neighbor-relationships. We can do this by drawing a mesh between centroids of touching neighbor cells.

mesh = cle.draw_mesh_between_touching_labels(cells)

cle.imshow(mesh)

We can also combine both visualizations in one image. Note, these images should not be used any further for quantitative analysis. It just serves visualization purposes.

Centroid connections and cell borders

A common way for visualizing tissues in this context is by drawing cell-borders and the centroid mesh in different colours.

visualization = mesh * 2 + cle.detect_label_edges(cells)

cle.imshow(visualization, color_map='jet')

Analyze and visualize number of touching neighbors

We can also count the touching neighbors and visualize the result as parametric image in colours.

neighbor_count_image = cle.touching_neighbor_count_map(cells)

cle.imshow(neighbor_count_image, color_map='jet', colorbar=True, min_display_intensity=0)

Note, the numbers along the image border may not be accurate. Hence, we should exclude the corresponding cells from the further analysis.

cells_ex_border = cle.exclude_labels_on_edges(cells)

cle.imshow(cells_ex_border, labels=True)

After correcting the label image, we can also correct the parametric image.

neighbor_count_image_ex_border = neighbor_count_image * (cells_ex_border != 0)

cle.imshow(neighbor_count_image_ex_border, color_map='jet', colorbar=True, min_display_intensity=0)

Now, we can measure the number of neighbors. We can either just read those numbers and put them in a list …

cle.read_intensities_from_map(cells_ex_border, neighbor_count_image_ex_border)

cl.Array([[0., 5., 6., 7., 6., 6., 7., 6., 6., 5., 5., 6., 6., 7., 6., 6.,
        6., 6., 6., 6., 6.]], dtype=float32)

… we can also read these values together with all other statistics and put them in a pandas DataFrame.

statistics = cle.statistics_of_labelled_pixels(neighbor_count_image_ex_border, cells_ex_border)

table = pd.DataFrame(statistics)

# rename a column
table = table.rename(columns={"mean_intensity": "number_of_neighbors"})

# only filter out a subset of all columns; only what we care
table = table[["label", "number_of_neighbors", "centroid_x", "centroid_y"]]

table

	label	number_of_neighbors	centroid_x	centroid_y
0	1	5.0	74.592697	23.731028
1	2	6.0	173.741379	35.582230
2	3	7.0	49.460915	51.928082
3	4	6.0	91.783768	52.666199
4	5	6.0	142.728210	62.962471
5	6	7.0	189.973206	68.526794
6	7	6.0	73.699181	88.797356
7	8	6.0	115.321083	90.665649
8	9	5.0	163.097733	99.824242
9	10	5.0	58.206852	122.341309
10	11	6.0	98.847565	134.280228
11	12	6.0	147.731705	127.326218
12	13	7.0	200.522903	112.817368
13	14	6.0	67.880905	162.991592
14	15	6.0	122.943306	157.515717
15	16	6.0	171.010025	153.333328
16	17	6.0	43.426266	189.492981
17	18	6.0	96.272728	192.326477
18	19	6.0	140.815964	194.446030
19	20	6.0	193.817596	193.019318

Exercise

Analyze a larger field of view with more cells and vary the parameters random_sigma_x and random_sigma_y of the artificial_tissue_2d function. Use a touching-neighbor-count map to count the number of touching neighbors before and after applying a median filter to the map.